We could start guessing the approximate value of this hypothetical "superpawn" or "enhanced pawn" in terms of "mobility", in the order of E~2P because of the definition (move up to 2 squares instead of only 1 square).
Next we adjust this initial guess by forming an 8x8 matrix, where each square has a number indicating how "mobile" is the analyzed piece (P=pawn, E="enhanced pawn") when placed at that square:
Pawn xxxxxxxx<--last rank Enhanced pawn xxxxxxxx
22222222<--first rank 22222222
Pawn xxxxxxxx Enhanced pawn xxxxxxxx
Here we have an average mobility of 2 squares for the enhanced pawn vs 7/6 for the normal pawn (who can only jump 2 squares when located at the initial rank). The relative power E/P appears to be 2/(7/6)=12/7~1.7 slightly below E=2P.
But there are normally other pieces that populate the board and limit the mobility. In a real game, we will find that at some locations our new "superpawn" is completely surrounded by other pieces and does not differ from a "normal pawn". So the tentative number E=1.7P should be pushed somewhat lower.
In order for these numbers to be of any value, we should imagine certain tasks or situations and see how a particular piece or group of pieces performs.
A similar analysis has been made for the standard chess pieces. Some examples:
- 1 Queen cannot corner and checkmate a lonely rival King, while 2 Rooks can.
That suggests 2R>Q which is in accordance with the normally accepted values Q~9P, R~5P. (Or Q~10P R~5.5P).
- King+Rook can checkmate an enemy King, while kNight+Rook cannot (they need the aid of the King). So in this case K+R>N+R, K>N.
- But a kNight can cross a barrier formed by a Rook, while a King cannot. So there are opposite situations where N>K.
For some tasks K>N, for other tasks N>K. This behaviour is supported by the official point scales, which evaluate the difference of King vs kNight to be in the order of a pawn or fraction of pawn.
And where does our new enhanced pawn fit? He can cross the barrier of a rook, while a King cannot. That means that in some situations, he can outperform a King, E>K (being K between ~3P and ~4P)
- But he cannot cross a barrier formed by 2 Rooks, while a Bishop can. So here is B>E.
- And he cannot cross a barrier formed by 2 Bishops, while a kNight can. So here is N>E.
- If we build a big table with lots of tasks, we can count how many "E>K" and how many "K>E", "E>B", "B>E"...etc we have, and calculate an average.
A more powerful approach would be to access a big database of complete games, not just individual "tasks".
As has been already mentioned in this site, with the aid of a game database it is possible to analyze the result of trading pieces. Applying this idea to our "superpawns", with thousands of games we could answer questions like "Is a superpawn really worth 2 pawns? Or is 2P>E?
The player who loses 1E while taking 2P from the rival, does he normally lose? Or does he retain a reasonable expectation of winning?
What about 2E vs 3P? E vs B? 2E vs B? 2E vs N?
It is often said that everything depends on the position, but with big (very big!) sets of data we could think that the variations of particular positions tend to cancel out and what remains after averaging is what we call "piece value".